Category Modeling, Simulation & Wargaming

People keep referencing us on the 3-to-1 Rule

Several people in their articles have referenced a 3-to-1 rule and then reference us as the source. The latest example is in a German article on Taiwan: Storming Taiwan by force of arms? | Telepolis

Of course, we are the people who are saying the 3-to-1 rule is really not correct. They obviously do not read that far.

This is the reference they use: The Source of the U.S. Army Three-to-One Rule – The Dupuy Institute. My final sentence in that article is “Are we training the next generation of George B. McCellans?”


Various links related to the 3-to-1 rule:

Trevor Dupuy and the 3-1 Rule – The Dupuy Institute

The U.S. Army Three-to-One Rule – The Dupuy Institute

The 3-to-1 Rule in Histories – The Dupuy Institute

The 3-to-1 Rule in Recent History Books – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 243 Battles 1600-1900 – The Dupuy Institute

The U.S. Army Three-to-One Rule versus 49 U.S. Civil War battles – The Dupuy Institute

The U.S. Army Three-to-One Rule versus the 752 Case Division-level Data Base 1904-1991 – The Dupuy Institute

Summation of Force Ratio Posts – The Dupuy Institute

JSTOR, Trevor Dupuy, Combat Data and the 3:1 Rule – The Dupuy Institute

The 3:1 Ratio – The Dupuy Institute

Army- and Division-level force ratio posts – The Dupuy Institute

The 3-to-1 rule and the War in Ukraine – The Dupuy Institute

We have been talking about this for a while. It appears that some people are not listening.




The 40% Rule

Hadn’t done a blog post in the while. Been focused on getting a book done. Sorry.

There is a rule of thumb often quoted out there and often put in war games that a unit becomes ineffective or reaches a breakpoint at 40% casualties. The basis for this rule is a very limited body of studies and analysis.

First, I have never seen a study on when a unit become ineffective. Even though it is now an accepted discussion point, I have not seen such a study establishing this relationship and do not think that such a study exists. I am not saying that there is not a relationship between casualties and unit effectiveness, what I am saying that I have never seen a study establishing that 1) this relationship exists, and 2) what are its measurements, and 3) what is the degree of degradation.

What has been done is studies on breakpoints, and over time, a rule of thumb that at 40% a unit “breaks” appears to be widely accepted. It appears that this rule has then been transferred to measuring unit effectiveness.

The starting point for “breakpoints” study is Dorothy Clark’s study of 43 battalions from World War II done in 1954. That study showed that the average casualties for these battalions was around 40%, although the ranged from around 1% to near 100%. Her conclusion was that “The statement that a unit can be considered no longer combat effective when it has suffered a specific casualty percentage is a gross oversimplification not supported by combat data.” She also stated “Because of wide variations in data, average loss percentages alone have limited meaning.”. We have discussed this before, see: C-WAM 4 (Breakpoints) | Mystics & Statistics ( and April | 2018 | Mystics & Statistics ( and Breakpoints in U.S. Army Doctrine | Mystics & Statistics ( and Response 3 (Breakpoints) | Mystics & Statistics (

The next point is the U.S. Army’s Maneuver Control manuals (FM 105-5) which in 1964 set the attacker’s breakpoint at around 20 percent casualties and the defender’s breakpoint at around 40 percent at the battalion-level. Charts in the 1964 Maneuver Control field manual showed a curve with the probability of unit break based on percentage of combat casualties. Once a defending unit reached around 40 percent casualties, the chance of breaking approached 100 percent. Once an attacking unit reached around 20 percent casualties, the chance of its halting (type I break) approached 100 percent, and the chance of its breaking (type II break) reached 40 percent. These data were for battalion-level combat. 

We have never found any studies establishing the data for these Maneuver Control manuals and we do not think they exist. Something may have been assembled when they were writing these manuals, but we have not been able to find any such files. Most likely, the tables were extension of the Dorothy Clark study, even though she said that it should not apply.

Anyhow, that is kind of it. Other stuff had been published on breakpoints, Helmbold in 1972, McQuie in 1987 (see: Battle Outcomes: Casualty Rates As a Measure of Defeat | Mystics & Statistics ( and Dupuy in the late 1980s, but I have not seen anything of significance since, as it appears that most significant studies and analysis work stopped around 1989. 

Now, Dr. Richard Harrison, who spends a lot of time translating old Soviet documents, has just sent me this: 

“Supposing that for the entire month not a single unit will receive reinforcements, then we will have a weakening of 30%, with 70% of the troops present. This is a significant weakening, but it does not yet deprive the unit of its combat strength; the latter’s fall begins approximately with losses of 40%.”

His source is: 

N.N. Movchin, Posledovatel’nye Operatsii po Opytu Marny i Visly (Consecutive Operations on the Experience of the Marne and Vistula) (Moscow and Leningrad: Gosudarstvennoe Izdatel’stvo, 1928), page 99.

So, the U.S. came up with the 40% rule in 1954 which it disowned and then adopted in 1964 regardless. And here we have a 1928 Russian writing which is directly applying a 40% rule to unit effectiveness. I have no idea what the analytical basis is for that statement, but it does get my attention.  

Let’s talk about artillery shells

Now, when we first did the validation database the Ardennes Campaign Simulation Data Base, one of the fields we had to fill in for each division, and corps, and army was on the tons of ammunition used each day by four types.

This was because the combat models that were supposed to be validated using this database were used in part to determine the number of shells needed for a predicted upcoming war. Back in 1987, when we started this database, it was a war in Europe versus the Soviet Union and the Warsaw Pact.

Now, my history with the Concepts Analysis Agency (CAA), later renamed the Center for Army Analysis (still CAA), goes back to 1973, when it was founded in Bethesda, MD. I was in my junior year in high school, my mother had just been promoted to a school principal and my father had just finished his three-year assignment in the Pentagon. My mother did not want to move again, so, my father found another assignment in the DC area. This was with the newly forming CAA in 1973. He had just happened to have finished a master degree in Systems Analysis from USC, so was nominally qualified.

My father was working over at manpower in the Pentagon, under Col. John Brinkerhoff. They all reported to General Donn Starry (who I did have the pleasure of meeting). Those two transferred together over the CAA, with Col. (Dr.) John Brinkerhoff taking over a division with my father as his assistant. I therefore started hearing stories about CAA combat models in 1973 based upon my father’s hands-on experience. One of the stories he told was that the model tended to fire the longest-range weapons first as units were closing. This made the 8″ Howitzer very valuable. In fact, so valuable, that the best wargaming strategy was build an army of 8″ Howitzers and destroy the Warsaw Pact before they could ever get into engagement range. Obviously, there were a couple of flaws in that wargame.

But, the suite of models, some of which are still in use today, was used to determine the ammunition requirements for the U.S. Army. Therefore, a validation database needed to address these issues. The same fields also existed the Kursk Data Base (1993-1996), which ended up never being used to validate a combat model. It was used to create a big-ass book.

Anyhow, CAA combat models did determine our ammunition requirements until the end of the cold war (22 or 25 or 26 December 1991 when the Soviet Union fell). They were also used to determine the requirements for the 1991 Gulf War. According to the story I heard in a meeting, CAA provided the Army general staff with the requirements for the Gulf War. The general staff doubled the figures CAA gave and then we stacked every dock in the Gulf with ammunition. Luckily none of Hussian’s missiles hit those docks. At the end of the war, it turns out we shipped at least ten times the ammunition we needed. As this was old dumb munitions dating back to World War II, it was cheaper to destroy them there then ship them back, which is what we did. Don’t have a count of what was destroyed in the Gulf, but guessing it was millions of rounds. 

After that, I do not know what OSD PA&E or CAA or the U.S. Army did to determine ammunition requirements. We no longer had a neatly canned scenario like the Fulda Gap. We no longer had a clear enemy. How much ammunition is needed is driven by both the combat model used (which tends to “run hot”) and more significantly, the scenarios used. If all the scenarios used a four-day combat scenario (like the Gulf War) then one will end up with very different needs then if one is planning for a 90-day or 180-day war (or three-year war in the case of Ukraine). I have no idea what scenarios were used, and it is probably classified. But, the end result, is that our production of ammunition over the decades since 1991 has dropped considerably while a lot of our reserves were destroyed in the Gulf.

This, of course, harkens back to a complaint I have made over the years, which is that we tend to focus on the missions and wars we think are most likely now, and not the entire spectrum of wars and conflicts that we can see are possible if one looks wider and deeper into history. Clearly, we were not ready for extended war in Ukraine, and this is not the first time in recent times we have not been properly prepared for certain conflicts. I do discuss this issue in America’s Modern Wars. 

P.S. The West is underestimating Ukraine’s artillery needs – Defense One

Interesting review of The Battle for Kyiv

Just stumbled last night across this review of The Battle for Kyiv. It is an interesting take on the subject. The reviewer is someone I know.

Draft history in The Battle of Kyiv: The Fight for Ukraine’s Capital by Christopher A. Lawrence – Armchair Dragoons

Now, my nagging suspicion is that it will be a while (decades) before anything other than a “draft” history can be written. Might be more than a few decades to get access to Russian archives. We were not able to get access to Soviet archives on Kursk (1943) until 1993, and that was only by using some round about means and a project budget not available to most historians. We have still not gotten access to Chinese records from the Korea War (1950–1953). So, one is certainly looking at least at 50 to 75 years in these cases.

Measuring Unit Effectiveness in Italy

We are in discussion over revisiting the measurement of combat effectiveness of select units in Italy 1943-1945. This was done by Trevor Dupuy in Numbers, Predictions and Wars (1977) by division using the QJM (Quantified Judgment Model) and was done in aggregate by me in War by Numbers (2017) using simply comparative statistics. If you feel lifeless reading blogs like this, you can rest for a bit through sites such as 홈카지노.

For a little background on page 115 of Understanding War is a chart of German, UK and U.S. units in the Italian Campaign and their CEVs (Combat Effectiveness Values). Their values range from 0.60 to 1.49. The German Hermann Goering Division is the highest rated division at 1.49. This is based upon five engagements. The German 3rd PzGrD was rated 1.17 based upon 17 engagements and 15th PzGrD was rated 1.12 based upon 11 engagements. This was done using the QJM.
    For reference, I would recommend reading the following four books:
1. Understanding War
2. War by Numbers
3. Attrition (optional)
4. Numbers, Predictions and War (optional)
There are two ways to measure combat effectiveness. 1) Do a model run and compared the results of the model run to historical data. This requires 1) a historically validated combat model (there are very few), and 2) confidence in the model. 2) The other option is to do a statistical comparison of a large number of engagements. This is what I did in Chapters 5, 6 and 7 of War by Numbers.
One can measure combat effectiveness by three means: 1) Casualty effectiveness, 2) special effectiveness (distance opposed advance) or 3) Mission effectiveness. This is all discussed in Trevor Dupuy’s work and in War by Numbers.
To date, the only people I am aware of who have published their analysis of combat effectiveness is Trevor Dupuy, me (Chris Lawrence) and Niklas Zetterling. See: CEV Calculations in Italy, 1943 | Mystics & Statistics ( and his book Normandy 1944 (recently revised and republished). There is also a six-volume quantitative effort related to Operation Barbarossa by Nigel Askey, which I have never looked at. Everyone else has ignored quantifying this issue, although there are no shortage of people claiming units are good, bad or elite. How they determine this is judgment (and it is often uncertain as to what the basis is for this judgment).
Now, the original work on this was done by Trevor Dupuy in the late 1970s based upon his data collection and the QJM. Since that time the model has been updated to the TNDM. The engagements used for the QJM validation were then simplified (especially in weapons counts) and assembled into the LWDB (Land Warfare Data Base). The LWDB had around 70 engagements from the Italian Campaign. Since that time we have created the DuWar series of databases which includes the DLEDB (Division-Level Engagement Data Base). See: The History of the DuWar Data Bases | Mystics & Statistics ( We have doubled the number of Italian Campaign engagements to around 140.
There are a total of 141 Italian Campaign division-level engagements in the DLEDB. The first 140 engagements cover from September 1943 to early June 1944. There is almost 12 months of war not covered and not all units in the first part of the campaign are covered. With all the various nationalities involved (i.e German, Italian, U.S., UK, Free French, Moroccan, New Zealand, South African, Poland, Indian, Canadian, Brazilian, Greek, etc.), the Italian Campaign is a fertile field for this work. We are looking at stepping back into this. 
Units involved in engagements in the DELDB:
3rd PzGrD: 25 cases
15th PzGrD: 39 cases
16th PzD: 7 cases
26th PzD: 8 cases
29 PzGrD: 6 cases
65th ID: 5 cases
94th ID: 8 cases
305th ID: 4 cases
362nd ID: 3 cases
715th ID: 2 cases
4th Para D: 3 cases
HG PzGrD: 26 cases
LXXVI Pz Corps: 4 cases
12th Para Rgt: 1 case
1st AD: 3 cases
3rd ID: 19 cases
34th ID: 15 cases
36th ID: 12 cases
45th ID: 20 cases
85th ID: 7 cases
88th ID: 4 cases
509th PIB: 1 case
1st SSF: 1 case
7th AD: 6 cases
1st ID: 9 cases
5th ID: 2 cases
46th ID: 18 cases
56th ID: 24 cases

Top Ten Blog posts in 2023

Happy New Year to all. 2023 is over. Not the best year for many in the world. Wanted to take a moment to list out our top ten blog posts for 2023 (based upon number of hits). They are:

  1. Wounded-to-killed ratios in Ukraine in 2022 | Mystics & Statistics (
  2. U.S. Tank Losses and Crew Casualties in World War II | Mystics & Statistics ( – a blog post by Dr. Shawn Woodford from 2016.
  3. How many brigades did Ukraine start with war with? | Mystics & Statistics ( – this is actually clipped from my book The Battle for Kyiv.
  4. Population over Time (US vs USSR) | Mystics & Statistics ( – a blog post from 2018. I suspect this gets so many hits because this was the initial entry point for a number of people who periodically check on this blog and they continue to use this post to direct them to our blog.
  5. German versus Soviet Artillery at Kursk | Mystics & Statistics ( – another 2018 blog post.
  6. New WWII German Maps At The National Archives | Mystics & Statistics ( – a 2017 blog post by Dr. Shawn Woodford.
  7. How Does the U.S. Army Calculate Combat Power? ¯\_(ツ)_/¯ | Mystics & Statistics ( – another 2017 blog post by Dr. Shawn Woodford.
  8. Tank Loss Rates in Combat: Then and Now | Mystics & Statistics ( – a 2016 blog post by Dr. Shawn Woodford.
  9. U.S. Army Force Ratios | Mystics & Statistics ( – a 2018 blog post.
  10. The Russian Artillery Strike That Spooked The U.S. Army | Mystics & Statistics ( – a 2017 blog post by Dr. Shawn Woodford. It was the second most popular blog post in 2022.

Honorable mentions:

13. Wounded-To-Killed Ratios | Mystics & Statistics ( – this 2016 blog post was our most popular blog post in 2022.

16. Where Did Japan Go? | Mystics & Statistics ( – this 2018 blog post was sort of the culmination of our series of demographic blog posts. May revisit this subject again this year.

18. The Russo-Ukrainian War – Day 560 | Mystics & Statistics ( – for a while we did post daily (then two-three times a week) about the war in Ukraine. This was our most popular one of those posts. We will probably restart these again sometime this winter, like when there is a danger of the front lines again moving.


Anyhow, the blog has been quieter for the last three months. This was in part because I was on travel and in part because I needed to finish up a book (The Siege of Mariupol). To date, I have not learned how to multi-task and complete a book, so the book has had the priority. Sorry to anyone I have not responded to as a result.

The Battle for Kyiv book will be available in the U.S. on come 18 January 2024.

Current book release schedule

I have four books in process or about to be released. They are:

The Battle for Kyiv:
– UK release date: 28 November
– U.S. release date: 18 January 2024

Aces at Kursk:
– UK release date: 30 January 2024
– U.S. release date: posted as 18 January 2024, but suspect release date will be in March 2024.

Hunting Falcon:
– UK release date: 28 February 2024
– U.S. release date: posted as 29 February 2024, but suspect released date will be in April 2024.

The Siege of Mariupol:
– UK release date: sometime in 2024
– U.S. release date: sometime in 2024

Books under consideration for 2024/2025:
The Battle for the Donbas
The Battle of Tolstoye Woods (from the Battle of Kursk)
More War by Numbers

Wargaming 101 – Summary

Chip Sayers has posted a number of articles to this blog under the title of “Wargaming 101.” He had lots of hands-on experience in the bowels of the Pentagon, so I found this to be a particularly interesting series of posts. He will be making a presentation at the second Historical Analysis Annual Conference (HAAC) on 18 October 2023. The presentation is called Wargaming 101. See: Schedule for the Second Historical Analysis Annual Conference (HAAC), 17 – 19 October 2023 | Mystics & Statistics (

Anyhow, as a read ahead, all of his Wargaming 101 blog posts are listed below:

Wargaming 101: The Use of Wargames in Training | Mystics & Statistics (

Wargaming 101 – Sayers vs. The U.S. Navy | Mystics & Statistics (

Wargaming 101 – The 40-60-80 Games | Mystics & Statistics (

Wargaming 101 – The 40-60-80 Games | Mystics & Statistics (

Wargaming 101: The Bad Use of a Good Tool | Mystics & Statistics (

Wargaming 101: A Tale of Two Forces | Mystics & Statistics (


A couple supporting posts:

“The Games the Marine Corps Plays” | Mystics & Statistics (

A story about planning for Desert Storm (1991) | Mystics & Statistics (


Also, we are still looking for presentations for the 2nd HAAC: Call for Presentations for the Second Historical Analysis Annual Conference (HAAC), 17-19 October 2023 | Mystics & Statistics (

Weaponising Historical Analysis – Dr. James Storr

The sixth briefing of the day was Weaponing Historical Analysis by Dr. James Storr. He is the author of three well received books.

Concerning my book War by Numbers, one reviewer stated that:

A great deal of the value of the book to the reader will depend upon how much that reader needs to see the data to believe. If one is prepared to accept the word of an expert, then Jim Storr’s The Human Face of War is the better book and the better read and presents much the same conclusions in briefer form – it would definitely be more suited to the average reader. On the other hand, for the reader that needs to see the numbers, this (along with Rowland and Biddle) is the must read. And for those most interested in the subject, both are very rewarding in different ways.

Anyhow, we only have less than 17 minutes of his presentation. Then the Zoom video recording stopped because it does not record for more than six hours, unbeknownst to us. So we missed the rest of his presentation. What we have is here: (9) Weaponising Historical Analysis: Storr – YouTube

His slides are here: Presentations from HAAC – Weaponizing Historical Analysis: A Case Study of the Introduction of HA Into Doctrine | Mystics & Statistics (

The recording ends of the slide titled “Factors,” which is slide 18 out of 32.  You will have to go here to catch the rest of the slides: HA-Conference-DC-Sep-22-V1.2.ppt ( Sorry, nature of self-funded conferences, we don’t employ professional audio-visual people. 

Killing Captain Hindsight – Dr. Niall MacKay

Our fifth presentation of the day was Killing Captain Hindsight: Quantifying Chance in Military History by Dr. Niall MacKay of the University of York.

It is posted to our YouTube Channel here: (9) Killing Captain Hindsight: MacKay – YouTube

The briefing ends at 57:40 and then there is five minutes of discussion afterwards.

The slides for the briefing are here: Presentations from HAAC – Killing Captain Hindsight: Quantifying Chance in Military History | Mystics & Statistics (